Capacitance meters are used in the art to measure a dielectric property of a fluid. Often, based on one or more measurements of a dielectric property, another property of the fluid can be determined.
A particular application of capacitance meters is in obtaining a pictorial representation of a property of a fluid over a cross-section of the conduit, e.g. the dielectric constant or the spatial distribution of a particular component of a multi-component fluid. In the specification the word ‘image’ is used to refer to such a pictorial representation. A multi-component fluid is a fluid comprising more than one component, for example a well fluid produced from an underground formation, which well fluid can comprise hydrocarbon oil, water, and/or natural gas.
Methods that provide an image of the fluid based on capacitance measurements using a capacitance meter are often referred to as capacitance tomography. Well known in the art are methods for calculating an image from the capacitances measured by the capacitance meter, for example linear back projection wherein the image is calculated by a series of linear operations on the capacitances.
A capacitance meter for capacitance tomography is disclosed in European patent specification with publication No. 0 326 266 B1. The known capacitance meter comprises an annular capacitance sensor arranged around a conduit. The capacitance sensor comprises eight sensor electrodes, which are arranged around the circumference of the conduit. Capacitances between any two single sensor electrodes are measured, wherein each capacitance measurement samples an average dielectric constant in the space probed by the respective electrodes. From the measurements an image consisting of K pixels can be constructed, wherein a pixel represents an average value of the dielectric constant in a discrete space element in the cross-section, the pixel data. Such an image can be transformed into a concentration image or a density image.
If the fluid is flowing through the conduit, it is often highly desirable obtain measurements of a flow property in addition to an image. In a publication by R. Thorn et al. in Flow Meas. Instrum. Vol. 1, October 1990, pages 259-268, it has been disclosed, how a flow velocity profile of the fluid can be obtained. To this end, the capacitance meter comprises two annular capacitance sensors located upstream and downstream along the conduit. Using each annular capacitance sensor, images Pu and Pd are determined repeatedly during a time interval. The flow velocity profile is determined from cross correlations of pixel data Pu,k of images determined during the time interval at the upstream sensor with pixel data Pd,l determined during the time interval at the downstream sensor. The cross correlation of pixel data, in the form of numbers representing for example density, can be described by             (                        P                      u            ,            k                          *                  P                      d            ,            l                              )        ⁢          (      t      )        =            1      T        ⁢                  ∫        0        T            ⁢                                    P                          d              ,              l                                ⁡                      (            s            )                          ⁢                              P                          u              ,              k                                ⁡                      (                          t              -              s                        )                          ⁢                                   ⁢                  ⅆ          s                    wherein
k,l are integers, wherein 1≦k,l≦K and K is the number of pixels in an image;
(Pu,k*Pd,l)(t) is the cross correlation of pixel data at a selected time t;
Pu,k(t−s) is the number associated with pixel k of an image provided by the upstream sensor at time (t−s);
Pd,l(s) is the number associated with pixel l of an image provided by the downstream sensor at time s; and
T is the duration of a correlation time window during the time interval.
Note, that this and other equations in this specification relating to cross-correlation calculations are written in integral form; it will however be clear to the skilled person how to calculate cross correlations using discrete measurements.
The method described in the publication is referred to as cross-correlation capacitance tomography. If the fluid is a multi-component fluid, other flow properties such as the volumetric or mass flow rates of a particular component can be determined from a concentration or density image and a flow velocity profile.
There are, however, a number of problems associated with capacitance flow meters, that have so far hampered their practical application in an industrial environment. For example, specific requirements for applications in the oil industry, where the flow of a multi-component fluid is to be monitored, have not yet been met. One requirement relates to the speed of operation. For cross-correlation capacitance tomography, processing of large amounts of data is required.
Consider the case that both the upstream and the downstream capacitance sensors contain N sensor electrodes. In known sensors N is typically in the order of 8 to 12. A complete data set of capacitances measured between all pairs of single sensor electrodes at a single annular capacitance sensor consists of in the order of N2 measured capacitances (more precise N(N−1)/2 capacitances). From this data set an image is calculated consisting of in the order of (N2)2=N4 pixels. To determine a complete flow velocity profile, a large number of images need to be determined during a time interval at both capacitance sensors, and all possible cross correlations between pixel data of each image plane must be calculated. This task requires then in the order of N8 cross-correlation operations. This presents an immense computational challenge requiring high-performance data-processing devices, e.g. special purpose devices such as a parallel-processor. Thus, in the absence of a far more efficient method for processing the data, the need for high-performance data-processing devices will impede the practical application in an industrial environment.
U.S. Pat. No. 5,396,806 discloses a method and apparatus for determining the mass-flow rate of a component in a two-component slurry mixture. The mass-flow rate is determined as the product of volume fraction of the component and overall flow velocity. The volume fraction is derived from the capacitance of the mixture, which capacitance is measured using a single annular capacitance sensor comprising a number of electrodes. Measurements using different pairs of electrodes are averaged in order to reduce the effects of non-uniformities of the flow patterns. The flow velocity is derived from triboelectric measurements, by cross-correlation of signals measured by an upstream and a downstream triboelectric probe.
It is an object of the present invention to provide an efficient method and capacitance meter for determining a flow property of a fluid flowing through a conduit by using capacitance flow meter.